The paper addresses the challenge of constructing conforming finite element spaces for the curl div operator in three dimensions. Tangential-normal continuity is introduced in order to develop distributional finite element curl div complexes. The spaces constructed are applied to discretize the quad curl problem, demonstrating optimal order of convergence. Furthermore, a hybridization technique is proposed, demonstrating its equivalence to nonconforming finite elements and weak Galerkin methods.

翻译：本文致力于解决三维空间中旋度散度算子的协调有限元空间构造难题。通过引入切向-法向连续性，建立了分布有限元旋度散度复形。所构造的空间被应用于四旋度问题的离散化，证明了其具有最优收敛阶。此外，提出了一种杂交技术，论证了其与非协调有限元及弱伽辽金方法的等价性。